Question

For the line segment whose endpoints are X (1, 2) and Y (6, 7), find the x coordinate for the point located 1 over 3 the distance from X to Y.

Answer 1

Answer:

$P = (\frac{8}{3},\frac{11}{3})$

Step-by-step explanation:

Given

$X = (1,2)$

$Y = (6,7)$

Required

The point at 1/3 of XY

If the point is at 1/3 for X, then the other end (to Y) is 2/3

So, we have:

$m:n = 1/3:2/3$

Multiply by 3

$m:n = 1:2$

The point (P) is calculated using:

$P = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

This gives:

$P = (\frac{1*6 + 2*1}{1+2},\frac{1*7 + 2*2}{1+2})$

$P = (\frac{8}{3},\frac{11}{3})$